Question

Write the coordinates of the image of each point by reflection in,

1. The $x-axis$
2. The $y-axis$
3. The line $y=x$ (Hint: Refer to the Example on page 578)

Point D.

Short answer

1. $R_{x-axis}:D=(-2,1)\to (-2,-1)$
2. $R_{y-axis}:D=(-2,1)\to (2,1)$
3. $R_{y=x}:D=(-2,1)\to (1,-2)$

Step-by-step solution

a.Step 1. Given Information.

Coordinate of point D is $(-2,1)$

Step 2. Explanation.

Image of $(-2,1)$ in the x-axis is $(-2,-1)$

Step 3. Conclusion.

So, the image of D in the $x-axis$is $R_{x-axis}:D=(-2,1)\to (-2,-1)$

b.Step 1. Given Information.

Coordinate of point D is $(-2,1)$

Step 2. Calculation.

Image of $(-2,1)$ in the y-axis is $(2,1)$.

Step 3. Conclusion.

So, $R_{y-axis}:D=(-2,1)\to (2,1)$.

c.Step 1. Given Information.

Coordinate of point D is $(-2,1)$

Step 2. Calculation.

Image of $(-2,1)$ in the line $x=y$ is $(1,-2)$

Step 3. Conclusion.

Therefore, $R_{y=x}:D=(-2,1)\to (1,-2)$.